Higher order differential lift equations over manifolds (Q1367650)

This paper is of a technical nature. It studies two types of tangential resolutions for a differentiable manifold \(M\) modeled on a Banach space (real or complex), namely the full tangential resolution \((T^k(M), \pi_k)_{k \geq 0}\) of iterated tangent bundles and a restricted tangential resolution suggested by \textit{R. H. Bowman} [Tensor, New Ser. 21, 139-150, 261-264 (1970; Zbl 0179.27202, Zbl 0192.59102)]. In an earlier paper, the present author [\textit{R. Greg Pond}, Int. J. Theor. Phys. 36, No. 3, 715-741 (1997; Zbl 0873.58002)] has demonstrated that the full tangential resolution context is not the appropriate framework for the consideration of higher order differential lift equations defined by vector fields. In the present paper he shows, among other things, that every differential lift equation formulated in the full tangential resolution context can be formulated and fully treated in the (simpler) Bowman context.